Finite-Agent Stochastic Differential Games on Large Graphs: I. The Linear-Quadratic Case
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917085938974720 |
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| author | Hu, Ruimeng Long, Jihao Zhou, Haosheng |
| author_facet | Hu, Ruimeng Long, Jihao Zhou, Haosheng |
| contents | In this paper, we study finite-agent linear-quadratic games on graphs. Specifically, we propose a comprehensive framework that extends the existing literature by incorporating heterogeneous and interpretable player interactions. Compared to previous works, our model offers a more realistic depiction of strategic decision-making processes. For general graphs, we establish the convergence of fictitious play, a widely-used iterative solution method for determining the Nash equilibrium of our proposed game model. Notably, under appropriate conditions, this convergence holds true irrespective of the number of players involved. For vertex-transitive graphs, we develop a semi-explicit characterization of the Nash equilibrium. Through rigorous analysis, we demonstrate the well-posedness of this characterization under certain conditions. We present numerical experiments that validate our theoretical results and provide insights into the intricate relationship between various game dynamics and the underlying graph structure. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_09523 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite-Agent Stochastic Differential Games on Large Graphs: I. The Linear-Quadratic Case Hu, Ruimeng Long, Jihao Zhou, Haosheng Optimization and Control 91A15, 91A43, 49N1 In this paper, we study finite-agent linear-quadratic games on graphs. Specifically, we propose a comprehensive framework that extends the existing literature by incorporating heterogeneous and interpretable player interactions. Compared to previous works, our model offers a more realistic depiction of strategic decision-making processes. For general graphs, we establish the convergence of fictitious play, a widely-used iterative solution method for determining the Nash equilibrium of our proposed game model. Notably, under appropriate conditions, this convergence holds true irrespective of the number of players involved. For vertex-transitive graphs, we develop a semi-explicit characterization of the Nash equilibrium. Through rigorous analysis, we demonstrate the well-posedness of this characterization under certain conditions. We present numerical experiments that validate our theoretical results and provide insights into the intricate relationship between various game dynamics and the underlying graph structure. |
| title | Finite-Agent Stochastic Differential Games on Large Graphs: I. The Linear-Quadratic Case |
| topic | Optimization and Control 91A15, 91A43, 49N1 |
| url | https://arxiv.org/abs/2406.09523 |